Leave-One-Out Least Square Monte Carlo Algorithm for Pricing American Options

The least square Monte Carlo (LSM) algorithm proposed by Longstaff and Schwartz (2001) is widely used for pricing American options. The LSM estimator contains undesirable look-ahead bias, and the conventional technique of removing it necessitates doubling simulations. We present the leave-one-out LSM (LOOLSM) algorithm for efficiently eliminating look-ahead bias. We also show that look-ahead bias is asymptotically proportional to the regressors-to-simulation paths ratio. Our findings are demonstrated with several option examples, including the multi-asset cases that the LSM algorithm significantly overvalues. The LOOLSM method can be extended to other regression-based algorithms improving the LSM method.